Paddy's Parts manufactures specialized parts for oil rigs and relies on job costing to cost their inventory. At the beginning of the year, management determined the following related to part #$81$:

Budgeted

Total Overhead $$350,000$

Cost Allocation Base Machine Hours

Machine Hours $50,000$

Direct Material per part $$10$

Beginning of Year Balances

Raw Material $$20,000$

Work in Process $$15,000$

Finished Goods $$27,000$

Cost of Goods Sold $$0$

At the end of the year, Paddy's produced $55,000$ parts, using $$495,000$ of raw materials and $$425,000$ of overhead. In the process, they used $52,000$ machine hours.

Required:

a$)$ Calculate the predetermined allocation rate for manufacturing overhead.

b$)$ Calculate the amount of overhead allocated. Close the factory overhead account by using the "write$-$off" to COGS approach. Show all of your journal entries. $($NOTE: Only enter the amount of overhead allocated in the box below. Show your journal entry and any calculations related to it on your separately$-$submitted work paper$)$